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 zpoequb.f(3) LAPACK zpoequb.f(3)

zpoequb.f -

# SYNOPSIS

## Functions/Subroutines

subroutine zpoequb (N, A, LDA, S, SCOND, AMAX, INFO)

ZPOEQUB

# Function/Subroutine Documentation

## subroutine zpoequb (integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)

ZPOEQUB
Purpose:
``` ZPOEQUB computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A and reduce its condition number
(with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
```
Parameters:
N
```          N is INTEGER
The order of the matrix A.  N >= 0.
```
A
```          A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N symmetric positive definite matrix whose scaling
factors are to be computed.  Only the diagonal elements of A
are referenced.
```
LDA
```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).
```
S
```          S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
```
SCOND
```          SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.
```
AMAX
```          AMAX is DOUBLE PRECISION
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
```
INFO
```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the i-th diagonal element is nonpositive.
```
Author:
Univ. of Tennessee
Univ. of California Berkeley
NAG Ltd.
Date:
November 2011
Definition at line 114 of file zpoequb.f.

# Author

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